document.write( "Question 93557: find each product university of phoenix elementary and intermediate algebra (3ypower2 + 1) 3y power 2-1) \n" ); document.write( "
Algebra.Com's Answer #68123 by bucky(2189)\"\" \"About 
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Given:
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\n" ); document.write( "\"%283y%5E2%2B1%29%283y%5E2-1%29\"
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\n" ); document.write( "Once you get familiar with this you remember this factoring form:
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\n" ); document.write( "\"%28a%5E2+-+b%5E2%29+=+%28a+%2B+b%29%28a+-+b%29\"
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\n" ); document.write( "This form says that if you have the difference of two squares, it factors into the product
\n" ); document.write( "of two factors, one the sum of the square roots of the squares and one the difference
\n" ); document.write( "of their square roots.
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\n" ); document.write( "What this problem gives you is the sum and difference factors, and you take them back to the
\n" ); document.write( "original term by recognizing that you square each term in the factors and subtract them.
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\n" ); document.write( "So if you quickly spot this pattern, you can tell yourself that the square of \"3y%5E2\" is
\n" ); document.write( "\"9y%5E4\" and the square of \"1\" is \"1\", so the original expression obtained from
\n" ); document.write( "multiplying the two terms you were given is \"9y%5E4+-+1\".
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\n" ); document.write( "But let's multiply out what you were given to get the product. Start with the given expressions
\n" ); document.write( "of:
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\n" ); document.write( "\"%283y%5E2%2B1%29%283y%5E2-1%29\"
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\n" ); document.write( "To do this multiplication you take the first factor of \"%283y%5E2+%2B1%29\" and you use (one at a time)
\n" ); document.write( "its two terms to multiply the second factor of \"%283y%5E2+-+1%29\". So you begin by taking the
\n" ); document.write( "\"3y%5E2\" from the first factor and you use it to multiply the second factor. In other
\n" ); document.write( "words you do the following distributed multiplication:
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\n" ); document.write( "\"3y%5E2%2A%283y%5E2+-+1%29\"
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\n" ); document.write( "This means you multiply the \"3y%5E2\" times each of the two terms in parentheses
\n" ); document.write( "to get:
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\n" ); document.write( "\"3y%5E2%2A%283y%5E2+-+1%29+=+9y%5E4+-+3y%5E2\"
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\n" ); document.write( "and you remember this result.
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\n" ); document.write( "Next you go back to the second term in the first factor ... the +1. And you use that term
\n" ); document.write( "to also multiply the second factor. In other words you do the following distributed
\n" ); document.write( "multiplication:
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\n" ); document.write( "\"1%2A%283y%5E2+-+1%29\"
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\n" ); document.write( "This means you multiply the \"1\" times each of the two terms in parentheses
\n" ); document.write( "to get:
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\n" ); document.write( "\"1%2A%283y%5E2+-+1%29+=+3y%5E2+-+1\"
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\n" ); document.write( "Now you combine this result with the previous result you were to remember and you get:
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\n" ); document.write( "\"9y%5E4+-+3y%5E2+%2B+3y%5E2+-1\"
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\n" ); document.write( "Notice that the two middle terms are equal but have opposite signs. Therefore, they cancel
\n" ); document.write( "each other out and you are left with the answer of:
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\n" ); document.write( "\"9y%5E4+-1\"
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\n" ); document.write( "Hope this isn't too confusing to you. Once you see the multiplication pattern it becomes
\n" ); document.write( "pretty easy to work problems such as these ... just take the terms in the first factor
\n" ); document.write( "and one at a time use them to multiply each of the terms in the second factor. Then
\n" ); document.write( "combine the results of all the products that you end up with. This same process will work
\n" ); document.write( "for multiplying other types of factors such as multiplying:
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\n" ); document.write( "\"%28a+%2B+b%29%2A%28c%2Bd%2Be%29\" or
\n" ); document.write( "\"+%28a%2Bb%2Bc%29%2A%28d%2Be%2Bf%29\" or
\n" ); document.write( "\"+%28a%2Bb%2Bc%29%2A%28d%2Be%2Bf%2Bg%29\"
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\n" ); document.write( "Just use each of the terms in the first factor to multiply the second factor and when you
\n" ); document.write( "are done, just combine all the products you got.
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\n" ); document.write( "Hope also that this helps you to see the logical pattern in multiplying factors. \n" ); document.write( "
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